If your child is smart enough to win a full scholarship, they must be at level of maturity that is higher than your average duck.
My daughter is currently 16, and I regularly share what her 529 balance with her, as I want her to learn about power of compounding interest. (I also have a separate brokerage account her also, which is comprised of mainly birthday and holiday money.)
We are very open about finances, and she knows that we will not be signing for college debt for her, However, I also want her to understand the results of her choices in life. That said, I have indicated that if she is careful about how she chooses her path through college, (i.e state schools, living at home the first year or 2, etc), that if she had money leftover in the 529 after she graduated, that I would pay the taxes and penalty, and sign the balance over to her to begin an IRA, and to provide her with some cash to start her life debt-free. She is understands this very clearly, and is beginning to chart a path.
I think that many kids don't receive proper guidance with finances, as their parents are just as financially illiterate. Because of this, they accept going into debt for college as 'normal', and are not mature enough to understand the damage this causes to their future.